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Math world stunned by UNH lecturer's find

Yitang Zhang, a lecturer in mathematics at the University of New Hampshire

DURHAM - Since 1999, Yitang "Tom" Zhang, 57, has been unassumingly teaching calculus classes at the University of New Hampshire as a well-liked lecturer.

He is not a tenure-tracked professor, and therefore is not required to publish or produce any research, but earlier this year, he made one of the greatest discoveries regarding a math problem that has been discussed since the time of Euclid.

Zhang helped the field get closer to proving or disproving the "Twin Prime Conjecture," which says there are an infinite number of prime numbers that are only two numbers apart.

Zhang's discovery demonstrated that the number of prime pairs that are less than 70 million units apart is infinite. He picked the number 70 million arbitrarily, and that difference has now been reduced to 600.

"Nobody had known before his work that there was any number that occurred as the difference of primes infinitely often. That is because primes simply occur with such irregularity," said Edward Hinson, chairman of the UNH Mathematics Department and an associate professor in mathematics.

The discovery was so big that the Annals of Mathematics notified Zhang within three weeks of receiving his report that they would be publishing it, an exceptionally quick turnaround time for such a journal. Within three days of that notification, Zhang was already speaking at Harvard University about his discovery.

Zhang said he was surprised at how rapidly refinements of his discovery have been made.

"I couldn't expect something could be done much better like this (this quickly)," Zhang said.

It has been just six short months since news of the discovery broke, and since then Zhang has been busy traveling, speaking and working with scholars around the world.

He said he has not enjoyed the busy schedule and traveling so much and does miss teaching, in part because of the challenges teaching undergraduate students presents.

"I have to explain the information very clearly, very organized - this is the way I like," said Zhang, who grew up in China and has a strong accent.

Hinson said it was clear all along that alongside teaching, Zhang had been doing serious mathematical research, and the discovery, and the accolades Zhang is receiving as a result, are the fruit of all that.

On Jan. 16, Zhang will be awarded the 2014 Frank Nelson Cole Prize in Number Theory at the American Mathematical Society's Joint Mathematics Meetings in Baltimore for his paper "Bounded Gaps between Primes." The prize is presented every three years and recognizes an outstanding research paper in number theory that has appeared in the preceding six years.

"That is the highest honor in the American mathematics community and in particular my major, number theory, this is very high. I am very happy," Zhang said.

Zhang is also a 2013 recipient of the Ostrowski Prize, which is awarded every other year by the Ostrowski Foundation in Switzerland for outstanding achievements in pure mathematics.

Zhang's discovery was certainly a surprise, not least of all because he was heretofore an unknown, 58-year-old researcher in New Hampshire who had published only twice before.

Zhang was born in China and earned his master's degree there at Peking University. He came to the United States in 1985 to earn his Ph.D. at Purdue University and came to New Hampshire in 1999 after earning a job as a lecturer at UNH.

Zhang said his interest in mathematics began when he was a child under the age of 10.

"I read some books. These books were for high school students, but when I was in elementary school, I read them," Zhang said during a recent phone interview.

He did not want to go into detail, but according to a story in the fall edition of UNH Magazine, Zhang lived through a difficult period in China. His family was "exiled to the countryside during Mao's Cultural Revolution and forced to perform hard labor,'' the magazine said. He couldn't attend school then, but studied on his own with "any book he could get his hands on.''

According to the magazine, as the revolution ended, Zhang enrolled in Peking University in 1978 and earned bachelor's and master's degrees. He then enrolled at Purdue, according to the magazine, and afterward worked as an accountant in Kentucky before being offered a position at UNH.He first started thinking about the Twin Prime Conjecture about four years ago.

"That was a very difficult problem at the very beginning. I tried lots of things but I couldn't find success," Zhang said. "Last summer, I found a certain way."

He said finding the one thing that opened the door came through trial and error of many, many methods, and was a culmination of knowledge and experience with the problem.

Hinson said prime numbers are one of the more relatively easy concepts of math to understand.

"It is simply a question of which numbers have whole number factors and which don't," Hinson said.

It was known for a very long time, since Euclid himself almost 2,500 years ago, that there were an infinite number of prime numbers, Hinson said, and the Greeks studied this, as well. The question has been where the primes are located among the numbers.

"It is a very difficult problem about a very simple concept, so everyone could understand the problem, but nobody could get at it," Hinson said. "What Tom had done then was to give yet another refinement of, in some ways, several thousand years' worth of work on this problem, but enough to give it a significant push - enough to put it in the realm of where people now see the possibilities for solution of the Twin Prime Conjecture itself."

He said that is by no means imminent, and some people believe the potency of the methods used by Zhang may run out before the final goal is reached, even Zhang himself.

Zhang said solving the Twin Prime Conjecture should prove to be a very tough problem, and he is not sure if it will be solved within his lifetime.

"And it will be the next Tom Zhang that will eventually arrive at it, but who knows for sure," Hinson said. "This was such a surprise to the mathematical community, you have to be open to other surprises."

Hinson said it is hard to make the case for the discovery having an immediate impact or technological consequence in terms of the average person's daily life, but the problem has been so fundamental that the impact and attention have been monumental and broad.

"This is a story of an unknown researcher doing these things which really gives it all the more resonance," Hinson said.

Hinson said UNH has had its share of mathematical successes and luminaries in the past, including former department Chairman Ken Appel, who was a co-solver of the famous four-color map theorem, and other prolific researchers, including Kevin Short, who has been involved in a variety of successful start-up companies.

Although Zhang's paper is currently available through the Annals of Mathematics online to those who have access, it will not appear in print until early next year.

In the spring, Zhang will spend a couple of months at the Institute for Advanced Study at Princeton University continuing mathematical research on something else entirely, which he said he was not yet ready to discuss.

Ultimately, he said, he does plan to return to New Hampshire, where he lives with his wife.